Jumping up and down: Denoiser diffusion models for discrete ordinal data
Abstract
Diffusion models are highly developed in continuous spaces for image and video domains. Recently, major advances have been made for discrete diffusion models for categorical data, specifically in the language domain. In contrast, diffusion models for discrete integer-valued data are less developed, despite the prevalence of this modality, ranging from images and music to gene counts. We introduce Jumping Up and Down (JUD)---a new family of denoiser-based diffusion models for discrete ordinal data. This is the first family of diffusion models for ordinal data which centers around training denoisers, which at the same time allows for bi-directional (up and down) perturbations of the data. The simplicity of the training objective, combined with the flexibility of bi-directional perturbations, leads us to obtain competitive results across different data modalities.
Related
- Up-down ordered Chinese restaurant processes with two-sided immigration, emigration and diffusion limits
- Blow-down and immediate onset of positivity in the Neumann problem for (super-)fast diffusion equations
- A stabilized scheme satisfying the discrete maximum principle for a time fractional convection-diffusion-reaction equation
- Gradient flow formulation and discrete approximation of reaction-cross-diffusion systems with size exclusion
- Binary Discrete Diffusion: Candidate-Set Diffusion for Logic and Planning Tasks
BibTeX
@misc{shenfeld2026jumping,
title = {{Jumping up and down: Denoiser diffusion models for discrete ordinal data}},
author = {Yair Shenfeld and Ricardo Baptista and Stefano Peluchetti},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02754},
eprint = {2610.02754},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02754},
}
RIS
TY - UNPB
TI - Jumping up and down: Denoiser diffusion models for discrete ordinal data
AU - Yair Shenfeld
AU - Ricardo Baptista
AU - Stefano Peluchetti
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.02754
UR - https://arxiv.org/abs/2610.02754
AB - Diffusion models are highly developed in continuous spaces for image and video domains. Recently, major advances have been made for discrete diffusion models for categorical data, specifically in the language domain. In contrast, diffusion models for discrete integer-valued data are less developed, despite the prevalence of this modality, ranging from images and music to gene counts. We introduce Jumping Up and Down (JUD)---a new family of denoiser-based diffusion models for discrete ordinal data. This is the first family of diffusion models for ordinal data which centers around training denoisers, which at the same time allows for bi-directional (up and down) perturbations of the data. The simplicity of the training objective, combined with the flexibility of bi-directional perturbations, leads us to obtain competitive results across different data modalities.
ER -